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arXiv · 1905.12358

The $κ$-(A)dS noncommutative spacetime

Angel Ballesteros·Ivan Gutierrez-Sagredo·Francisco J. Herranz
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Abstract

The (3+1)-dimensional $κ$-(A)dS noncommutative spacetime is explicitly constructed by quantizing its semiclassical counterpart, which is the $κ$-(A)dS Poisson homogeneous space. This turns out to be the only possible generalization of the well-known $κ$-Minkowski spacetime to the case of non-vanishing cosmological constant, under the condition that the time translation generator of the corresponding quantum (A)dS algebra is primitive. Moreover, the $κ$-(A)dS noncommutative spacetime is shown to have a quadratic subalgebra of local spatial coordinates whose first-order brackets in terms of the cosmological constant parameter define a quantum sphere, while the commutators between time and space coordinates preserve the same structure of the $κ$-Minkowski spacetime. When expressed in ambient coordinates, the quantum $κ$-(A)dS spacetime is shown to be defined as a noncommutative pseudosphere.

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Angel Ballesteros, Ivan Gutierrez-Sagredo, Francisco J. Herranz. 2019-07-18. The $κ$-(A)dS noncommutative spacetime. https://doi.org/10.1016/j.physletb.2019.07.038

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